$\left\{\begin{array} { l } y=20-2x \\ 6x-5y=12\end{array} \right.$
Move the variable to the right-hand side and change its sign$\left\{\begin{array} { l } y=20-2x \\ -5y=12-6x\end{array} \right.$
Divide both sides of the equation by $-5$$\left\{\begin{array} { l } y=20-2x \\ y=-\frac{ 12 }{ 5 }+\frac{ 6 }{ 5 }x\end{array} \right.$
Since both expressions $20-2x$ and $-\frac{ 12 }{ 5 }+\frac{ 6 }{ 5 }x$ are equal to $y$, set them equal to each other forming an equation in $x$$20-2x=-\frac{ 12 }{ 5 }+\frac{ 6 }{ 5 }x$
Solve the equation for $x$$x=7$
Substitute the given value of $x$ into the equation $y=-\frac{ 12 }{ 5 }+\frac{ 6 }{ 5 }x$$y=-\frac{ 12 }{ 5 }+\frac{ 6 }{ 5 } \times 7$
Solve the equation for $y$$y=6$
The possible solution of the system is the ordered pair $\left( x, y\right)$$\left( x, y\right)=\left( 7, 6\right)$
Check if the given ordered pair is the solution of the system of equations$\left\{\begin{array} { l } 2 \times 7+6=20 \\ 6 \times 7-5 \times 6=12\end{array} \right.$
Simplify the equalities$\left\{\begin{array} { l } 20=20 \\ 12=12\end{array} \right.$
Since all of the equalities are true, the ordered pair is the solution of the system$\left( x, y\right)=\left( 7, 6\right)$